Question

The rigid bar DEF is supported by three wires as shown in the figure below. There is a concentrated load P at E. The wires are all made of steel with E 289809 MPa, a vield stress of 400 MPa, each has a cross-sectional area of 1000 mm2 and each has a length of 6m. The coefficient of thermal expansion α of the wires is 20x10-6 per℃ Write down the equation of compatibility for the elongations in the three wires. (3 marks) 1. 2. Write down the equilibrium equations involving the axial forces in the wires and 3. the load P. (3 marks) If the load P is 490 kN, find the forces and stresses in each wire. (3 marks) 4. If the load P is 490 kN, what are the axial forces in the wires if there is increase in the temperature of wire AD (wire 1) of AT, +30.625 °C.(3 marks) 5. What load P combined with an increase in the temperature of wire AD (wire 1) of = +30.625 °C will cause the most highly stressed wire to reach yield. (3 marks) What is the maximum load P that can be carried? (3 marks) 6. 7. If the increase in the temperature of wire 1 is AT-+30.625 °C and wire 3 is the temperature change has no effect on the axial forces in the wires? (2 marks) 1 6m T-+30.605 °C, what increase in temperature is required in wire 2, 7, so that 10m BY Cy Rigid Figure 1

Answer 1

Given Compatibility equahon© Axial force CF- Change in leng th ơf- co ire AD or elona ahơn ge i Length f coive. A D ono 月D, L-AD AD E A S i mi Lar ly BE BE 61 BE C F E A s the en ter ap plied, ccentrica em ce e Lon call be highe.γ thorn that of AP.

6 SLBE CF BE AD Applying the condition ơf-similar triangles Compaki bilit 16 sl LO . 'AD A E L,A,E are the wires CF -2

の And applying the cosnaihơn ,of e7wili brium, A D Required equili boium ces. sub stituting value o_finh he aboveeaua hon A D 2-66下·BE テ 13.667- PRE Now, when P 400 kN, Solving equahơn cnd。) POPE 410 2 20o KN C. F tơn rom ea A D IRO N

e D 20x10 Stress m BE BE Louo PCE 10

When temperature- of- col,re AD -IT,タ+30,625 ℃ S L 6Les A D 3 E CF A D A E TAD + 3.6チ5- A E A D lo B E Ap. A D 367s AE A E AE A D BE looox2 0000

AD. From PAD in Hhe above qwahins Suwbstihuting value. BE. BE